Question

A lift is tied with thick iron wire and its mass is $1000kg$. If the maximum acceleration of the lift is $1.2ms$${}^{-2}$ and the maximum stress of the wire is $1.4$ x $10$${}^8$ Nm${}^{-2}$, what should be the minimum diameter of the wire ?

• A. 10${}^{-2}$ m
• B. 10${}^{-4}$ m
• C. 10${}^{-6}$ m
• D. 0.5 x 10${}^{-2}$ m

Answer 1

The correct option is A 10${}^{-2}$ m

$Stress\times area=M(g+1.2)$
$1.4\times {10}^8\times \frac{\pi }{4}{d}^2=1000\left(11\right)$
$d^2=\frac{1000\left(11\right)\times 4}{\pi \times 1.4\times {10}^8}$
$d=\sqrt{\frac{4\times 1000\left(11\right)}{\pi \times 1.4\times {10}^8}}$
$d=\sqrt{\frac{{10}^4}{{10}^8}}$
$={10}^{-2}m$